The present invention relates to a magnetic well for confining or containing a plasma--i.e., an ionized gas. Such wells are useful, for example, for plasma confinement in nuclear fusion reactors, as well as other areas.
A plasma in a magnetic field will tend to drift to the weakest region of the field. Therefore a field which increases in an outward direction from the plasma will be best suited to keep the plasma together--i.e., "confined". Such field configurations are collectively known as magnetic wells.
The theory of a constricted gas current was first developed by W. H. Bennett in 1934 in his article in Phys. Rev., Vol. 45, P. 890. A few years later, a different approach was presented independently by L. Tonks Electrochem. Soc., Vol. 72, p. 167 (1937). Tonks theoretically analyzed the constriction of a current filament due to the action of the azimuthal magnetic field generated by the current itself, the effect of constriction was called the "pinch effect". Subsequently, a great number of experiments involving pinch discharges have been carried out and the theory of a pinch discharge is well developed.
Because of the loss of charged particles from the ends of a linear pinch, endless tubes of either toroidal or race-track form were studied, see, for example, W. H. Bostick, USAEC Report Wash-115, Wash., D. C., 1952, or J. L. Tuck, USAEC Report Wash-146, Wash., D. C., 1953. "AEC" stands for Atomic Energy Commission. But even if losses along the field lines are inhibited by using toroidal configurations where the lines close upon themselves inside the confinement region, particles may be lost through drift motions across the magnetic field. Losses of this type can be minimized, either by choosing a magnetic field where the drift motions cancel for particles running through the confinement region repeatedly, such as in a stellarator machine as described by L. Spitzer, "Magnetic Fields and Particle Orbits in a High-Density Stellerator", AEC Report NYO-997, New York Operations Office, 1952, or by having drift motions which follow closed paths inside the same region, see B. Lehnert, Nature, London Vol. 181, p. 331 (1958), or N. C. Christofilos, Proc. Second Inter. Conf. on the Peaceful Uses of Atomic Energy, Vol. 32, p. 279 (1958).
Another concept of confining plasma is the magnetic mirror system which is used to minimize the loss of charged particles from the ends when a plasma is confined by means of an externally applied axial magnetic field in a straight cylindrical tube, R. F. Post, Proc. Second Int. Conf. On The Peaceful Uses of Atomic Energy, Vol. 32, p. 245 (1958); M. Bineau, T. Consoli, P. Hubert, F. Prevot, P. Ricateau, and A. Samain, Nucl. Instr., Vol. 5, p. 282 (1959); M. Bineau, T. Consoli, P. Hubert, P. Prevot, P. Ricateau, Nucl. Instr., Vol. 5, p. 290 (1959).
In most systems, such as mentioned above, in which a plasma is confined by a magnetic field that surrounds it smoothly, i.e., without a discontinuity, there will be a tendency toward instability. A field where the field-plasma interface is everywhere convex on the side toward the plasma has been proposed to overcome this instability, H. Grad. USAEC Report Wash-289, Washington, D.C., 1955; NYO-7969, New York Operations Office, 1957; J. Berkowitz, K. O. Friedrichs, H. Goertzel, H. Grad, J. Killeen, and E. Rubin, Proc. Second U.N. Conf. On Peaceful Uses of Atomic Energy, Vol. 31, p. 171 (1958); B. B. Kadomtsev and S. I. Braginsky, Proc. Second U.N. Conf. On Peaceful Uses of Atomic Energy, Vol. 32, p. 233 (1958); C. L. Longmire, USAEC Report Wash-289, -289, Washington, D.C. 1955; J. L. Tuck, USAEC Report Wash-289, Washington, D. C., 1955. Systems with this kind of field are called cusped magnetic fields. The cusped systems generally have linear or cylindrical geometry and yield one- or two-dimensional confinement only.
Other confinement systems, such as the "mirror-type" magnetic field of "Baseball II" are known, see C. C. Damm, H. Berkner, W. S. Cooper III, K. W. Ehlers, A. H. Futch, G. W. Hamilton, J. E. Osher, R. V. Pyle, Fourth Conference on Plasma Physics and Controlled Nuclear Fusion Research, Madison, Wisconsin, CONF-710607-98, 1971. This was the first field with a considerable degree of three-dimensional symmetry; but it does not have a spherical symmetry, i.e., the field configuration is not very isotropic. The present invention provides a more nearly spherically symmetric magnetic field, with field lines that have characteristics of cusped magnetic field as well. In addition, the following patents are known: U.S. Pat. Nos. 3,214,342, 3,218,235, 3,230,145, 3,290,219, 3,442,758, 3,561,033, 3,523,206, 3,650,893, 3,663,360, 3,155,592, 3,663,362, 3,665,508, 3,708,391.
Magnetic wells used to date generally have had cylindrical or toroidal symmetry. A more uniform (or isotropic) symmetry is desirable. A spherical symmetry, i.e., a totally isotropic well configuration, would be best, but this is all but impossible to achieve as a practical matter. We have discovered how to achieve polyhedral symmetry, which comes closest to the spherical one. This is achieved by locating current-carrying coils on planes corresponding to the facets of a regular polyhedron that can be symmetrically circumscribed about or within a sphere (hereinafter simply called "regular polyhedrons"). There are five such polyhedrons: tetrahedron (four sides), cube (six sides), octahedron (eight), duodecahedron (12), and icosahedron (12).
One such coil or loop configuration is analyzed in detail and corresponds to a coil on each of the eight facets of an octahedron. In this way, each coil passes through three of the six geometric poles on a reference sphere, i.e., the points where each axis of rectangular coordinates concentric with the sphere would cut its surface. Thus, the coils are arranged into four opposing sets or pairs. The axis of each set of loops is angularly displaced from that of the other three sets as the three apexes of a regular tetrahedron. By arranging the loops in this manner, a magnetic field with tetrahedral symmetry will be produced.
The strength and direction of the resulting magnetic field have been calculated, and the motion of charged particles in this field has been studied. Experiments were also made to show the characteristics of this magnetic field.
The features and advantages of the present invention will become apparent from the following detailed description, together with the accompanying drawings.